Bound surface limits to a function

Consider the following plot of two surfaces

Plot3D[Sin[x y], x^3 + y, x, -1, 1, y, -1, 1, PlotRange -> x, -1, 1, y, -1, 1, z, -1, 1, Mesh -> None]

plot

How can I produce a plot where I limit the the surface plot of $sin(x y)$, to be shown only when its values are above $x^3+y$, or any other given function.

2 Answers
2

Plot3D[ConditionalExpression[Sin[x y], Sin[x y] > x^3 + y], x, -1, 1, y, -1, 1, PlotRange -> -1, 1, -1, 1, -1, 1, Mesh -> None]

enter image description here

To show both functions

Plot3D[ConditionalExpression[Sin[x y], Sin[x y] > x^3 + y], x^3 + y , x, -1, 1, y, -1, 1, PlotRange -> -1, 1, -1, 1, -1, 1, Mesh -> None, BaseStyle -> Opacity[.7]]

enter image description here

Plot3D[Sin[x y], x, -1, 1, y, -1, 1, PlotRange -> -1, 1, -1, 1, -1, 1, MeshFunctions -> Sin[# #2] - #^3 - #2 &, Mesh -> 0, MeshShading -> None, Automatic, BoundaryStyle -> None]

enter image description here

You can utilize the option RegionFunction for that:

RegionFunction

Plot3D[Sin[x y], x^3 + y, x, -1, 1, y, -1, 1, Mesh -> None, RegionFunction -> (x, y, z [Function] Sin[x y] > (x^3 + y)) ]

enter image description here

Equivalently: reg = BoundaryDiscretizeRegion[ImplicitRegion[Sin[x y] > (x^3 + y), x, -1, 1, y, -1, 1]]; Plot3D[Sin[x y], x, y ∈ reg]
– J. M. is computer-less♦
Oct 6 at 9:59

reg = BoundaryDiscretizeRegion[ImplicitRegion[Sin[x y] > (x^3 + y), x, -1, 1, y, -1, 1]]; Plot3D[Sin[x y], x, y ∈ reg]

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